Abstract
Despite their substantial appeal, closure principles have fallen on hard times. Both anti-luck conditions on knowledge and the defeasibility of knowledge look to be in tension with natural ways of articulating single-premise closure principles (Lasonen-Aarnio in Philos Stud 157–173, 2008; Schechter in Philos Stud 428–452, 2013). The project of this paper is to show that plausible theses in the epistemology of testimony (‘transmission theses’) face problems structurally identical to those faced by closure principles. First I show how Lasonen-Aarnio’s claim that there is a tension between single premise closure and anti-luck constraints on knowledge can be extended to make trouble for transmission theses. Second, I show how Schechter’s claim that there is a tension between single premise closure and the thought that knowledge is defeasible can be extended to make trouble for transmission theses. I end the paper by sketching the consequences of this trouble for the dialectic in the epistemology of testimony.
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Notes
I use here the lexicon of reductionism and anti-reductionism. Alternative lexicons (as opposed to distinctive taxonomies) have been proposed in which, for example, ‘fundamentalism’ takes the place of ‘anti-reductionism’ (Graham 2006). I prefer to avoid any suggestion of religiosity.
Lasonen-Aarnio does not exploit the ideology of ‘belief forming methods’ in her statement of ANTI- LUCK. Neither Lasonen-Aarnio’s arguments or my own depend on the omission of this ideology.
If endorsing a closure principle is being optimistic, it is the sort of optimism that comes in degrees: some closure principles make more modest claims than others. Both Williamson and Hawthorne formulate more optimistic theses about deduction than I do here—their preferred formulations make no reference to defeat (Hawthorne 2004; Williamson 2011). Note that to refuse to endorse a closure principle is not to deny the epistemic significance and interest of deduction. One might, for instance, think that generic statements about deduction capture the procedure’s behaviour more aptly than universally quantified claims with attached necessity operators.
More precisely, they have the form:
Necessarily, if S knows that p and A comes to believe that p solely on the basis of competent understanding of S’s testimony that p, and θ obtains then A knows that P,
where we have some grip on what it is for θ to obtain that is suitably independent of our grip on what it is for acceptance of testimony to be knowledge producing.
Some people use ‘transmission thesis’ in a much narrower way than I do, to pick out, say, just theses which deny that accepting testimony from an ignorant speaker can be knowledge producing. See, for example, Faulkner (2011), Wright (2015). Note too that the way I am understanding transmission theses, theories which claim to be neither reductionist or anti-reductionist count as transmission theses. See, for example, Lackey (2008), Faulkner (2011).
I have been talking about knowledge and knowledge producing processes. Both ANTI-LUCK and DEFEAT can be formulated as theses concerning justification, rather than knowledge. Similarly both transmission theses and closure principles can be formulated as theses about justification, as well as articulated in terms of knowledge. In this paper I will be talking primarily about the interaction between closure principles and transmission theses formulated as theses about knowledge. But each of the arguments considered here can be run, mutatis mundi, as an argument concerning the justification-centred incarnations of these theses.
Such reliability may or may not be rooted in a disposition to refrain from forming false beliefs. As Lackey has pointed out, a speaker may be a reliable testifier with respect to whether or not p even when their own beliefs as to whether or not p are hopelessly mistaken. In her case CREATIONIST TEACHER, she envisages a testifier whose testimony in the classroom is guided by the scientific consensus concerning the theory of evolution, but whose own beliefs are not so guided (Lackey 2008).
Given that Lasonen-Aarnio proposes that a deduction of q from p is competent ‘just in case’ conditions (i)–(iii) are met, it is most natural to read her as proposing (i)–(iii) as necessary and sufficient conditions rather than as merely necessary conditions.
Things get more complicated once we acknowledge that Lasonen-Aarnio says that ‘[t]he conditional [of condition (iii)]…could either be a logical entailment or a material implication’ (Lasonen-Aarnio 2008).One reason for preferring the latter reading, she says, is that it would let us give a unified account of deductive inference and inference more generally. But maybe we ought to prefer the former reading. Suppose I incompetently deduce q from the known premise p, where p is false in some close worlds. Lasonen-Aarnio envisages the worlds in which the deduction goes badly being evenly distributed across worlds in which p (and my belief that p) is true and worlds in which p (and my belief that p) is false. But if what it is for a deduction from p to go badly is for me to deduce some q* such that it is false that [not-p or q*] then a deduction from p cannot go badly in worlds in which p is false. If the proposition if p then q* is true whenever p is false, then any inference from p in a world in which p is false will count as a good inference. And in that case, in a case like BASKETBALL, all the bad inferences will be in worlds in which p is true and only 80 % of close worlds will be close worlds in which I truly believe that p and my inference is successful:
Truly believes p
Falsely believes p
Inference good
80 % of close worlds
10 % of close worlds
Inference bad
10 % of close worlds
0 % of close worlds
The point is not that if the consequences that I have outlined really are consequences of Lasonen-Aarnio’s proposed constraint on competent deduction, her argument fails to work. Even if they are consequences of her proposed constrain, risk will accumulate so as to make trouble for SPC. Rather, one might think that the conclusion we ought to draw from the above is that there is a certain triviality built into her proposed account of competent deduction when it is glossed this way: the proposed condition is too easily met to do the work of capturing what counts as a competent deduction. This concern replicates even if we gloss ANTI-LUCK in, say, reliabilist terms rather than using the rubric of safety. Suppose, as Lasonen-Aarnio proposes, that a reliabilist gloss of competent deduction of q from p will require a high ratio of cases in which some relevant proposition q* is inferred from some relevant proposition p* to be such that in those cases the material conditional if p* then q* is true. Such a constraint will be met whenever p* is false in a high ratio of cases, arguably trivialising it.
This problem - if it is one - can be avoided by having the conditional be an entailment rather than a material conditional. If this means we lack the prospect of a unified account of inference, so much the worse for unified accounts. But it is not clear that such a reading will avoid problems of its own. Presumably I can competently deduce that p from the premise that in the actual world, p. But it doesn’t look like the premise here entails the conclusion. Importantly for my purposes, whether or not we can resolve these puzzles about how to understand competent deduction does not affect the prospects for generating a case against transmission theories. The trouble (if there is any) is generated by the conditionals of (iii) and (iii’). But we don’t—as I show later—need to use a conditional when proposing an account of competent speech interpretation.
I take myself to be making good on what is noted in passing by Hawthorne and Lasonen-Aarnio that worries about objective chance that arise for closure principles also arise for testimonial (and preservative memory) transmission principles (Hawthorne and Lasonen-Aarnio 2009).
Note that the plausibility of thoughts (1)–(3) is not independent of one’s views on evidence. For example, if one thinks that an agent’s evidence is just those propositions that said agent knows (that is, that E = K) then whenever p is a proposition that I know, the epistemic probability that p will (on my evidence) be 1. Where q is some proposition that is entailed by a proposition that I know, the epistemic probability that q will (on my evidence) be 1 (Williamson 2000). If we go for this sort of story about evidence then there may well turn out to be cases where I ought (or so it seems) to have a low degree of confidence in propositions with an epistemic probability of 1. And such a picture does not sit easily with (2). Whether and how such an account might model an agent’s encountering evidence against propositions that they know is not clear: if E = K and I know that p then then there is no proposition q such that P(p/p&q) < 1. (Williamson 2000). If these sorts of considerations are enough to make you unsympathetic to the sort of picture codified in (1)–(3) much of the tension charted in this paper will fail to vex you. But even disinterested observers need not be uninterested. Note that puzzles with the same sort of structure as those produced by the Williamsonian picture do emerge on other, more standard views of evidence such as those that assign probability 1 to all logical truths: it seems plausible that there are circumstances in which I ought to have a low degree of confidence in some logical truth and if p* is a logical truth where P(p*) = 1 there will be no proposition q* such that P(p*&q*) < 1. (I thank an anonymous reviewer for this point.) Nevertheless, the Williamsonian picture seems to be in a deeper tension with defeat epistemology than those views which assign probability 1 to logical truths. Endorsing the latter view does not stop us from thinking that there are lots of cases in which I know propositions whose probability is less than 1. And if that is the case then, so long as we assume there is some threshold such that the probability of p on my evidence needs to be greater than n (where 0 < n < 1) for me to know that p, we can easily model the defeasibility of knowledge of propositions that don’t have probability 1. But for the Williamsonian there are no known propositions with a probability of less than 1.
Schechter runs his argument in terms of justification rather than knowledge. I have modified his cases so as to reflect this paper’s focus on knowledge.
Note that this last condition means that for all x where x > 1, if Sx knows the proposition that they tell Sx + 1 their belief in that proposition is solely based upon competent understanding of Sx − 1’s knowledgeable telling of that proposition. This is analogous to the idealising assumption implicit in SCHECHTER that Schechter knows all of his intermediate and final conclusions only if each of his deductions bestows knowledge.
But then, it may be that even once we strip away our grasp of what counts as knowledge we can tell a story about what it is for beliefs to avoid lucky truth. If this is so then a closure principle revised along these lines might retains the power and interest of simpler statements of single premise closure. Whether or not we should be optimistic about the prospects for such a revision depends on deep problems as to the proper way of thinking about anti-luck conditions on knowledge, which I am not in a position to address here.
This may depend on some details of how we understand circularity that are not noted here.
Of course, it might turn out that there are tensions not envisaged here between elements of the Williamsonian picture and the project of the transmission theorist.
I thank an anonymous reviewer for this point.
A historical note. In the 18th century Locke wrote: ‘A credible man vouching his knowledge of it, is a good proof, but if another, equally credible, do witness it from his report, the testimony is weaker; and a third that attests from hearsay of an hearsay, is yet less considerable. So that in traditional truths, each remove weakens the force of the proof: and the more hands the tradition has successively passed through, the less strength and evidence does it receive from them (Locke 1997). One way of thinking about this paper is as spelling out this Lockean thought in the ideology of contemporary epistemology (although it is unclear whether what Locke had in mind is captured better by the ideology of anti-luck or that of defeat).
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Acknowledgments
Thanks to Lizzie Fricker, John Hawthorne, Emil Moeller, and Timothy Williamson for their helpful discussion and comments. Particular thanks go to an anonymous reviewer for detailed and insightful comments on earlier drafts.
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Fraser, R.E. Risk, doubt, and transmission. Philos Stud 173, 2803–2821 (2016). https://doi.org/10.1007/s11098-016-0638-y
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DOI: https://doi.org/10.1007/s11098-016-0638-y